Charge transport steady-state measurements

FIGURE 22.6 Permeability and permselectivity of vaginal and buccal epithelia in the rabbit, (a) Flux of 6-carboxyfluoroscein, a hydrophilic molecule, by in vitro perfusion studies steady-state flux ( xg/cm2/h x 106), (b) resistance (fl cm2 x 10 2), (c) thickness (p,m x 10-2), and (d) ratio of potassium transport number to chloride transport number, which is calculated from electrical measurements, used as indicative of the epithelium selectivity for positively charged molecules. (Modified from Sayani, A.P. and Chien, Y.W., Crit. Rev. Ther. Drug Carrier Syst. 13, 85, 1996.)... 

Here, it should mention that the response time of electrokinetic transport of nanoparticles in a nanochannel is very fast, of about femtosecond [5], which is too fast to be measured by the current experimental methods. Therefore, understanding of the characteristics at a steady state will be sufficient for the appreciation of the elec-trokinetic motion of the nanoparticles in the nanochannels. In the following sections, it is assumed that the walls of the nanochannel and the surface of the nanoparticle are all negatively charged. 

The approximate experimental determination of xl), is based on measurement of the velocity of a charged particle in a solvent subjected to an applied voltage. Such a particle experiences an electrical force that initiates motion. Since a hydrodynamic frictional force acts on the particle as it moves, a steady state is reached, with the particle moving with a constant velocity U. To calculate this electrophoretic velocity U theoretically, it is, in general, necessary to solve Poisson s equation (Equation 3.19) and the governing equations for ion transport subject to the condition that the electric field is constant far away from the particle. The appropriate viscous drag on the particle can be calculated from the velocity field and the electrical force on the particle from the electrical potential distribution. The fact that the sum of the two is zero provides the electrophoretic velocity U. Actual solutions are complex, and the electrical properties of the particle (e.g., polarizability, conductivity, surface conductivity, etc.) come into play. Details are given by Levich (1962) (see also Problem 7.8). 

The RDE has the considerable practical advantage over techniques such as cyclic voltammetry, potential step, or a.c. methods. The rate of mass transport to the electrode may be varied over a substantial range and in a controlled way without resort to a rapid change in the electrode potential which inevitably leads to the measured current having a contribution from charging the double layer. Since in most experiments with the RDE only (pseudo) steady state currents are measured, the recorded current may be unequivocably equated with the faradiac current. 

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